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Theorem equtr 1595
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)

Proof of Theorem equtr
StepHypRef Expression
1 ax-8 1395 . 2  |-  ( y  =  x  ->  (
y  =  z  ->  x  =  z )
)
21equcoms 1594 1  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-17 1419  ax-i9 1423
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  equtrr  1596  equequ1  1598  equveli  1642  equvin  1743
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